The middle term in the expansion of ${(1 + x)^{2n}}$ is
$\frac{{(2n)!}}{{n!}}{x^2}$
$\frac{{(2n)!}}{{n!(n - 1)!}}{x^{n + 1}}$
$\frac{{(2n)!}}{{{{(n!)}^2}}}{x^n}$
$\frac{{(2n)!}}{{(n + 1)!(n - 1)!}}\,{x^n}$
In the expansion of ${(1 + x)^n}$ the coefficient of $p^{th}$ and ${(p + 1)^{th}}$ terms are respectively $p$ and $q$. Then $p + q = $
The coefficient of $x^{18}$ in the product $(1+ x)(1- x)^{10} (1+ x + x^2 )^9$ is
The coefficient of the term independent of $x$ in the expansion of $(1 + x + 2{x^3}){\left( {\frac{3}{2}{x^2} - \frac{1}{{3x}}} \right)^9}$ is
Find a positive value of $m$ for which the coefficient of $x^{2}$ in the expansion $(1+x)^{m}$ is $6$
In the expansion of ${\left( {{x^2} - 2x} \right)^{10}}$, the coefficient of ${x^{16}}$ is